Question

Expansion :if a+1/a=p prove that a³+1/a³=p(p²-3)

Answer 1

To prove
Cubing on both sides
So
(A+1/a)³=p³
A³+1/a³+3*a*1/a(a+1/a) =p³
A³+1/a³+3p=p³
A³+1/a³=p³+3p
A³+1/a³=p(p²-3)
Hence it is proved


I hope this will help you
By DEVANSH

Answer 2

Given

• a + 1/a = p

To Prove

• a³ + 1/a³ = p ( p² - 3 )

Proof

$\bf a+\dfrac{1}{a}=p$

cubing on both sides , we get ,

$\implies \bf a^3+\dfrac{1}{a^3}+3.a.\dfrac{1}{a}(a+\dfrac{1}{a})=p^3\\\\\implies \bf a^3+\dfrac{1}{a^3}+3(p)=p^3\\\\\implies \bf a^3+\dfrac{1}{a^3}=p^3-3p\\\\\implies \bf a^3+\dfrac{1}{a^3}=p(p^2-3)$

Hence proved